132 ANIMAL AGGREGATIONS 



12, 15, 20, and 30 mated pairs; two bottles held 50 mated pairs each; 

 and one bottle had 25 mated pairs. At the end of 8 days at 25° C. the 

 surviving parent flies were transferred to fresh bottles for a second 

 breeding period of 8 days. The only variable known to be significant 

 throughout this series was the density of the population. All the 

 offspring from the two breeding periods were counted and sexed. 

 The results tabulated as the rate of reproduction per female per day 

 during the first 16 days of life are shown in Figure 7. 



In this figure the circles give the observations, and the curve is the 

 graph of the following equation fitted by the method of least squares: 



>' = 34-S3 g~''-"l\;~°''58 J 



which in logarithmic form becomes: 



log y = i. S4 — 0. 008.V — 0.658 log X , 



when y signifies the flies per mated female per day and x is the num- 

 ber of mated flies per bottle, taken over the whole 16-day period the 

 experiment ran. 



The observations include a total of 23,922 progeny flies, which is 

 a large enough number to cause the results to be treated with re- 

 spect. Further, it is apparent that the curve fits the observed facts 

 closely. In the preceding chapter, I have called attention to the 

 fact that this formula is related to that which Bilski developed to 

 describe the effect of crowding on the rate of growth in tadpoles, to 

 that of Kennealy for the relation between length of race and the 

 record established for that distance, and to that of Farr for the rela- 

 tion between density of human population and the death-rate. These 

 phenomena must be based on a common fundamental biological 

 relationship. 



When these results are analyzed further, we find that the greatest 

 drop in rate of reproduction of adult flies per female per day comes as 

 the number of original mated pairs per bottle increases from i to 2, 

 and the next greatest drop comes between the bottles having an 

 initial population of 2 and 3 mated pairs. This result cannot be due 

 to larval crowding, since the bottles containing 9 mated pairs of flies 



